While children's development at five has improved, results at age seven remain unchanged, it says.

Although it acknowledges that there have been changes to free nursery education, and its link to children's results at the age of seven is not "straightforward", the NAO says the Department for Education "did intend that the entitlement would have lasting effects on child development throughout primary school and beyond".

Nationally, 59% of five-year-olds achieved a good level of development in 2010/11, compared with 45% in 2005/06, the report says.

But it adds: "National key stage 1 results, however, have shown almost no improvement since 2007, so it is not yet clear that the entitlement is leading to longer-term educational benefits."

The watchdog also warns that youngsters from poorer areas are still less likely to get access to good quality nursery care than those from wealthier homes.

In total, 95% of three- and four-year-olds are in early education – a rate that has been sustained since 2008, the report says.

But an analysis of Ofsted data, conducted by the NAO, found the percentage of good or outstanding nursery care in March last year ranged from 64% in some local authorities to 97% in others.

"Areas of highest deprivation were less likely to have high-quality provision," it found.

The NAO head, Amyas Morse, said: "The Department for Education needs to do more to put itself in the position to assess whether the forecast long-term benefits of free education for three- and four-year-olds are being achieved. It also needs to understand how the arrangements for funding providers of that early education drive its availability, take-up and quality.

"Both of these are necessary if it is to get the best return for children from the £1.9bn spent each year."

Under the scheme, all three- and four-year-olds are entitled to 15 hours of free education a week for 38 weeks a year. In January 2011, 831,800 youngsters were receiving this entitlement.

Daniela Wachsening, education policy adviser at the Association of Teachers and Lecturers (ATL), said: "There is absolutely no doubt that high-quality early years education makes a massive difference to children's development, and is particularly important for children from disadvantaged families.

"But the government is jeopardising the chances of disadvantaged children by cutting the grants to local authorities, which has led to the loss of high-quality early years places and drastic reductions in children's and family services to the detriment of the most vulnerable children."

The children's minister, Sarah Teather, said: "We are pleased that the NAO has recognised the progress made since we introduced free early education for three- and four-year-olds.

"There is lots more to do – and the report also sets out important national and local challenges to be addressed. We are determined to improve the availability of quality places in disadvantaged areas, and offering free early education to around 40% of two-year-olds will help by bringing even more money into the system.

"We also want to examine in more detail how to make sure the significant improvements we are seeing at five feed through into better results at seven."